Hamiltonian Monte Carlo methods for efficient parameter estimation in steady state dynamical systems

  • Kramer A
  • Calderhead B
  • Radde N
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Abstract

BACKGROUND: Parameter estimation for differential equation models of intracellular processes is a highly relevantbu challenging task. The available experimental data do not usually contain enough information toidentify all parameters uniquely, resulting in ill-posed estimation problems with often highly correlatedparameters. Sampling-based Bayesian statistical approaches are appropriate for tackling thisproblem. The samples are typically generated via Markov chain Monte Carlo, however such methodsare computationally expensive and their convergence may be slow, especially if there are strong correlationsbetween parameters. Monte Carlo methods based on Euclidean or Riemannian Hamiltoniandynamics have been shown to outperform other samplers by making proposal moves that take thelocal sensitivities of the system's states into account and accepting these moves with high probability.However, the high computational cost involved with calculating the Hamiltonian trajectories preventstheir widespread use for all but the smallest differential equation models. The further development ofefficient sampling algorithms is therefore an important step towards improving the statistical analysisof predictive models of intracellular processes.

RESULTS: We show how state of the art Hamiltonian Monte Carlo methods may be significantly improved forsteady state dynamical models. We present a novel approach for efficiently calculating the requiredgeometric quantities by tracking steady states across the Hamiltonian trajectories using a Newton-Raphson method and employing local sensitivity information. Using our approach, we compare bothEuclidean and Riemannian versions of Hamiltonian Monte Carlo on three models for intracellularprocesses with real data and demonstrate at least an order of magnitude improvement in the effectivesampling speed. We further demonstrate the wider applicability of our approach to other gradientbased MCMC methods, such as those based on Langevin diffusions.

CONCLUSION: Our approach is strictly benefitial in all test cases. The Matlabsources implementing our MCMC methodology is available fromhttps://github.com/a-kramer/ode_rmhmc.

Author-supplied keywords

  • Hybrid monte carlo
  • MCMC methods
  • Parameter estimation
  • Steady state data
  • Systems biology

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Authors

  • Andrei Kramer

  • Ben Calderhead

  • Nicole Radde

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